Let D be a directed graph of order n. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. We prove that if D is a directed graph with even order n and if the indegree and the outdegree of each vertex of D is at least 23n then D contains an anti-directed Hamilton cycle. This improves a bound of...

A k-factor of a graph is a k-regular spanning subgraph. A Hamilton cycle is a connected 2-factor. A graph G is said to be primitive if it contains no k-factor with 1 ≤ k < ∆(G). A Hamilton decomposition of a graph G is a partition of the edges of G into sets, each of which induces a Hamilton cycle. In this paper, by using the amalgamation technique, we find necessary and sufficient conditions f...